see, x=[x] +{x}.

now, use this:

(x+1) -[x+1] + 2x = 4[x+1] - 6

3x +7=5[x+1].

3x +7=5[x] + 5.

3x +2 = 5[x].

Now, draw the graphs of y=3x+2 and y=5[x].

the intersection points will give you the desired solutions. You can try hit n trial also.

like 8/3 and 1 are two solutions. I haven't checked for more.

but for clarity try to draw graphs.

If still any doubt exists, do tell us.